




'''simple docstring'''

from __future__ import annotations


def __UpperCAmelCase	(   _UpperCAmelCase		:   int						)      ->      list[int]:
			__snake_case			=		2
			__snake_case			=		[]
			while i * i <= n:
						if n % i:
									i += 1
						else:
									n //= i
									factors.append(_UpperCAmelCase						)
			if n > 1:
						factors.append(_UpperCAmelCase						)
			return factors


if __name__ == "__main__":
						import doctest

						doctest.testmod()






"""simple docstring"""


def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)				->   int:




						'''simple docstring'''



						def update_area_of_max_square(__lowerCAmelCase  ,       __lowerCAmelCase							) -> int:
												# BASE CASE
												if row >= rows or col >= cols:
																		return 0

												lowerCamelCase__   =update_area_of_max_square(__lowerCAmelCase  ,       col + 1							)
												lowerCamelCase__   =update_area_of_max_square(row + 1  ,       col + 1							)
												lowerCamelCase__   =update_area_of_max_square(row + 1  ,       __lowerCAmelCase							)

												if mat[row][col]:
																		lowerCamelCase__   =1 + min([right, diagonal, down]							)
																		lowerCamelCase__   =max(largest_square_area[0]  ,       __lowerCAmelCase							)
																		return sub_problem_sol
												else:
																		return 0

						lowerCamelCase__   =[0]
						update_area_of_max_square(0  ,       0							)
						return largest_square_area[0]





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)				->   int:




						'''simple docstring'''



						def update_area_of_max_square_using_dp_array(
						    __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							) -> int:
												if row >= rows or col >= cols:
																		return 0
												if dp_array[row][col] != -1:
																		return dp_array[row][col]

												lowerCamelCase__   =update_area_of_max_square_using_dp_array(__lowerCAmelCase  ,       col + 1  ,       __lowerCAmelCase							)
												lowerCamelCase__   =update_area_of_max_square_using_dp_array(row + 1  ,       col + 1  ,       __lowerCAmelCase							)
												lowerCamelCase__   =update_area_of_max_square_using_dp_array(row + 1  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)

												if mat[row][col]:
																		lowerCamelCase__   =1 + min([right, diagonal, down]							)
																		lowerCamelCase__   =max(largest_square_area[0]  ,       __lowerCAmelCase							)
																		lowerCamelCase__   =sub_problem_sol
																		return sub_problem_sol
												else:
																		return 0

						lowerCamelCase__   =[0]
						lowerCamelCase__   =[[-1] * cols for _ in range(__lowerCAmelCase							)]
						update_area_of_max_square_using_dp_array(0  ,       0  ,       __lowerCAmelCase							)

						return largest_square_area[0]





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)				->   int:




						'''simple docstring'''



						lowerCamelCase__   =[[0] * (cols + 1) for _ in range(rows + 1							)]
						lowerCamelCase__   =0
						for row in range(rows - 1  ,       -1  ,       -1							):
												for col in range(cols - 1  ,       -1  ,       -1							):
																		lowerCamelCase__   =dp_array[row][col + 1]
																		lowerCamelCase__   =dp_array[row + 1][col + 1]
																		lowerCamelCase__   =dp_array[row + 1][col]

																		if mat[row][col] == 1:
																								lowerCamelCase__   =1 + min(__lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)
																								lowerCamelCase__   =max(dp_array[row][col]  ,       __lowerCAmelCase							)
																		else:
																								lowerCamelCase__   =0

						return largest_square_area





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)				->   int:




						'''simple docstring'''



						lowerCamelCase__   =[0] * (cols + 1)
						lowerCamelCase__   =[0] * (cols + 1)
						lowerCamelCase__   =0
						for row in range(rows - 1  ,       -1  ,       -1							):
												for col in range(cols - 1  ,       -1  ,       -1							):
																		lowerCamelCase__   =current_row[col + 1]
																		lowerCamelCase__   =next_row[col + 1]
																		lowerCamelCase__   =next_row[col]

																		if mat[row][col] == 1:
																								lowerCamelCase__   =1 + min(__lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)
																								lowerCamelCase__   =max(current_row[col]  ,       __lowerCAmelCase							)
																		else:
																								lowerCamelCase__   =0
												lowerCamelCase__   =current_row

						return largest_square_area


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	print(largest_square_area_in_matrix_bottom_up(2, 2, [[1, 1], [1, 1]]))


